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Shock and Vibration
Volume 2015 (2015), Article ID 453216, 17 pages
Research Article

Stability Analysis of a Breathing Cracked Rotor with Imposed Mass Eccentricity

1Department of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
2School of Energy Power and Mechanical Engineering, China Electric Power University, Beijing 102206, China

Received 14 April 2015; Revised 8 June 2015; Accepted 15 June 2015

Academic Editor: Sundararajan Natarajan

Copyright © 2015 Huichun Peng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The investigation of the effects of mass eccentricity on stability of a gravity dominated cracked Jeffcott rotor would generally provide practical applicability to crack detection and instability control of the heavy loading turbo-machinery system. Based upon the numerical Floquet method, the stability and bifurcations of the periodic time-dependent rotor with a transverse breathing crack are studied with respect to the varied mass eccentricity at different rotation speed, and the stability diagrams in the parameter plane are obtained which the previous studies have not covered. The numerical response of the cracked rotor system is also analyzed by the frequency spectrum to present the vibration characters while the rotation speed approaches the critical ratio. The detailed numerical eigenvalues of the transition matrix are applied to analyze the types of the bifurcations of the cracked rotor system. Three types of bifurcations are found and responses of the cracked rotor system at these bifurcations are presented for the visualized comparisons.